Magnetic resonance imaging (“MRI”) is one of the most versatile and fastest growing modalities in medical imaging. As part of the MRI process, the subject patient is placed in an external magnetic field. This field is created by a main magnet assembly, which can be either closed or open. Open magnet assemblies have two spaced-apart magnet poles separated by a gap, and a working magnetic field volume located within the gap.
Gradient coils located within the gap superimpose linear gradients on the main magnetic field. A gradient coil can include conductors fixed in appropriate locations, such as etched on a printed circuit board.
The diagnostic quality of images produced by MRI is directly related to several system performance characteristics. One very important consideration is the uniformity, or homogeneity, of the main magnetic field. In order to produce high-resolution images, the magnetic field produced in the MRI scanner must be maintained to a very high degree of uniformity.
Magnetic fields that vary linearly with distance are needed to make MRI images. Designing the main magnet structure such that the poles are close to the imaging volume, and therefore close to the gradient coils, enhances the efficiency of the magnet. However, as the gradient coils are placed closer to the main magnet poles, undesirable interactions occur between them, which can be further complicated by the necessity to switch the gradients on and off rapidly. Eddy currents induced in conductive materials surrounding the MRI apparatus produce unwanted non-uniform fields that distort the desired gradient fields in time and space.
To eliminate eddy currents, additional gradient coils typically are used to cancel the field at the surrounding conductive regions while preserving the linear gradient field. The additional coils are called shields and together with the primary coils constitute self-shielded gradients.
First described is a conventional method used to design self-shielded gradients. For simplicity, planar gradients are assumed, but the method applies to cylindrical gradients as well.
A primary current distribution is represented by a series of terms
            J      s        =                  ∑        n            ⁢                          ⁢                        a          n                ⁢                              ϕ            n                    ⁡                      (                          x              ,              y                        )                                ,where φn (x,y) are current distribution components at particular locations and an are amplitudes of these components. Since J is a vector in a plane, the φn are vectors also. Each of the φn satisfies the continuity equation. φn(x,y) can be, for example, a two-dimensional Fourier series.
For each of the φn, a current density on a shielding surface is calculated that, for an infinite surface, would produce zero field on the outer side of the shield. The outer side refers to the side farthest from the imaging volume, toward the magnet pole. See FIG. 1, which shows the relative positions of the magnet poles 1, the imaging volume 2, the primary gradient currents 3, and the gradient shield currents 4.
To get zero field on the outer side of the shield, a current density is placed on the shield that would result if the outer side consisted of a superconductive material. In such a material the field is zero. Thus, applying Ampere's Law results in a current density on the shield surface of J= Ht, where Ht is the tangential component of the field of the primary coils.
Thus for each of the φn, we have both a primary current distribution and a shield current distribution. If the shield could extend to infinity, shielding would be perfect.
Using some kind of optimization procedure, the an are chosen such that a linear field is produced in the imaging volume. The an can be chosen to give a linear field at a set of points (the target field approach) or the an can null out non-linear components in an expansion representation of the field.
It would be advantageous to provide a method for producing a gradient field that is a substantially uniform gradient in the magnet gap and has a substantially zero value outside of a shield surface. It would also be advantageous to eliminate currents in the main magnet induced by the magnetic fields of the gradient coils.